Problem: Given $ m \angle MON = 9x + 45$, $ m \angle LOM = 8x - 23$, and $ m \angle LON = 107$, find $m\angle LOM$. $O$ $L$ $N$ $M$
Answer: From the diagram, we see that together ${\angle LOM}$ and ${\angle MON}$ form ${\angle LON}$ , so $ {m\angle LOM} + {m\angle MON} = {m\angle LON}$ Substitute in the expressions that were given for each measure: $ {8x - 23} + {9x + 45} = {107}$ Combine like terms: $ 17x + 22 = 107$ Subtract $22$ from both sides: $ 17x = 85$ Divide both sides by $17$ to find $x$ $ x = 5$ Substitute $5$ for $x$ in the expression that was given for $m\angle LOM$ $ m\angle LOM = 8({5}) - 23$ Simplify: $ {m\angle LOM = 40 - 23}$ So ${m\angle LOM = 17}$.